On the first 3 quizzes of his physics class, Christopher got an average score of 77. What does he need on the next quiz to have an overall average of 82?
Solution: Let his score on the next quiz be $x$ The sum of all of his scores is then $3 \cdot 77 + x$ The same sum must also be equal to $4 \cdot 82$ Solve: $x = 4 \cdot 82 - 3 \cdot 77 = 97$.